Top-K with a Heap

Keep only the largest k values by maintaining a small min-heap.

Algorithm

@steps

Store the heap in an array.
Compare parent and child indexes instead of building explicit tree nodes.
Swap only when the heap order is violated.
Print the deterministic final heap state for replay comparison. @end @complexity

Time: O(n log k)
Space: O(k) @end

bounded heap For top-k largest values, a min-heap of size k keeps the current cutoff at the root.

Ruby DSA Implementation

basic.rb

def list_string(values) = "[#{values.join(', ')}]"
def heap_insert(heap, value)
  heap << value
  child = heap.length - 1
  while child > 0
    parent = (child - 1) / 2
    break if heap[parent] <= heap[child]
    heap[parent], heap[child] = heap[child], heap[parent]
    child = parent
  end
end
def heap_pop(heap)
  smallest = heap[0]
  heap[0] = heap.pop
  parent = 0
  loop do
    left = parent * 2 + 1
    right = left + 1
    break if left >= heap.length
    child = right < heap.length && heap[right] < heap[left] ? right : left
    break if heap[parent] <= heap[child]
    heap[parent], heap[child] = heap[child], heap[parent]
    parent = child
  end
  smallest
end
heap = []
[5, 1, 9, 3, 7, 2].each do |value|
  heap_insert(heap, value)
  heap_pop(heap) if heap.length > 3
end
puts list_string(heap.sort.reverse)

@end @output [9, 7, 5] @end